Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms

Lee, Sukbin; Lebensohn, Ricardo A.; Rollett, Anthony D.

doi:10.1016/j.ijplas.2010.09.002

Cited by 83 publications

(44 citation statements)

References 53 publications

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“…It means that the macroscopic strain E is now considered as an unknown and is obtained at convergence. In (14), ∆ 0 (ξ) is the "stress Green's tensor", given, for ξ ̸ = 0, by:…”

Section: The Strain and Stress Based Iterative Schemesmentioning

confidence: 99%

“…The approach has been afterwards extended to non linear composites [21,15]. It have been used by the authors themselves but also by other researchers for computing the overall response of visco-elasto-plastic composites (see for instance [2,3,13,11,14]). The FFT based method [20] allows to expand the elastic solution into Neumann series, along the lines of a method which was first introduced for composite conductors by Brown [6] and later by Kroener [12].…”

Section: Introductionmentioning

confidence: 99%

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A polarization‐based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast

Monchiet

Bonnet

2011

Numerical Meth Engineering

161

199

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SUMMARY It is recognized that the convergence of FFT‐based iterative schemes used for computing the effective properties of elastic composite materials drastically depends on the contrast between the phases. Particularly, the rate of convergence of the strain‐based iterative scheme strongly decreases when the composites contain very stiff inclusions and the method diverges in the case of rigid inclusions. Reversely, the stress‐based iterative scheme converges rapidly in the case of composites with very stiff or rigid inclusions but leads to low convergence rates when soft inclusions are considered and to divergence for composites containing voids. It follows that the computation of effective properties is costly when the heterogeneous medium contains simultaneously soft and stiff phases. Particularly, the problem of composites containing voids and rigid inclusions cannot be solved by the strain or the stress‐based approaches. In this paper, we propose a new polarization‐based iterative scheme for computing the macroscopic properties of elastic composites with an arbitrary contrast which is nearly as simple as the basic schemes (strain and stress‐based) but which has the ability to compute the overall properties of multiphase composites with arbitrary elastic moduli, as illustrated through several examples. Copyright © 2011 John Wiley & Sons, Ltd.

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“…It means that the macroscopic strain E is now considered as an unknown and is obtained at convergence. In (14), ∆ 0 (ξ) is the "stress Green's tensor", given, for ξ ̸ = 0, by:…”

Section: The Strain and Stress Based Iterative Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A polarization‐based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast

Monchiet

Bonnet

2011

Numerical Meth Engineering

161

199

View full text Add to dashboard Cite

show abstract

“…The other technique recently developed is fast Fourier transform (FFT) proposed originally by Moulinec and Suquet [331] and further studied and improved in Ref. [332][333][334][335][336][337][338]. The initial idea of the method was to make direct use of the digital images of the real microstructure in the numerical simulation which reduces the effort to generate compatible microstructural finite element discretizations [331].…”

Section: Analysis At the Rve Levelmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

178

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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“…Usage of the spectral method approach based on the fast Fourier transform was pioneered by Moulinec and Suquet 24 and has gained significant attention in computational material mechanics. 25,26 Besides the computational performanceespecially when simulating periodic microstructures-one significant advantage of the spectral method is the straightforward use of experimental datasets consisting of regularly arranged measurement points. One drawback of the early spectral method variants, namely the poor convergence rate for materials with a high difference in stiffness or strength, has been overcome by the use of sophisticated root-finding algorithms instead of the original fix-point scheme.…”

Section: Numerical Solvermentioning

confidence: 99%

Coupled Crystal Plasticity–Phase Field Fracture Simulation Study on Damage Evolution Around a Void: Pore Shape Versus Crystallographic Orientation

Diehl

Wicke

Shanthraj

et al. 2017

JOM

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Various mechanisms such as anisotropic plastic flow, damage nucleation, and crack propagation govern the overall mechanical response of structural materials. Understanding how these mechanisms interact, i.e. if they amplify mutually or compete with each other, is an essential prerequisite for the design of improved alloys. This study shows-by using the free and open source software DAMASK (the Dü sseldorf Advanced Material Simulation Kit)-how the coupling of crystal plasticity and phase field fracture methods can increase the understanding of the complex interplay between crystallographic orientation and the geometry of a void. To this end, crack initiation and propagation around an experimentally obtained pore with complex shape is investigated and compared to the situation of a simplified spherical void. Three different crystallographic orientations of the aluminum matrix hosting the defects are considered. It is shown that crack initiation and propagation depend in a non-trivial way on crystallographic orientation and its associated plastic behavior as well as on the shape of the pore.

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Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms

Cited by 83 publications

References 53 publications

A polarization‐based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast

A polarization‐based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Coupled Crystal Plasticity–Phase Field Fracture Simulation Study on Damage Evolution Around a Void: Pore Shape Versus Crystallographic Orientation

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